Above the Influence: Kvothe finds it best if he doesn't follow up on Denna's request to join her for a swim in the lake after she's been subject to denner resin.
A Taste of the Lash: An important part of Kvothe's legend building is when he is flogged -a drug he takes beforehand to dull the pain has the side effect of constricting the blood vessels so he doesn't bleed, earning him the nickname "Kvothe the Bloodless"
Bookends: The silence of three parts is described at the start and the end of the book.
Broken Ace: Kvothe is brilliant and excels at everything he tries, but tears himself apart so badly in the process that by the time Chronicler finds him, he's a shadow of his former self.
Bullying a Dragon: Chronicler originally tries to bully/blackmail Kvothe to get his story. Around the point where Kvothe gets frustrated and a bottle eight inches from his hand explodes, it occurs to Chronicler that maybe this was a bad idea.
Call a Rabbit a "Smeerp": Not with real animals, but with fantastic ones: zombies and trolls are shamblemen and trow, for example.
Cannot Spit It Out: Played perfectly straight. Kvothe is afraid of throwing himself at Denna because of the number of boy friends she's had. He thus does not confess his true feelings to her. He is unable to even when she is high on denner resin (a drug similar to opium) and thus unlikely to note or remember anything he says.
Chekhov's Gun: Exposition and important future plot points get mentioned in stories the characters tell.
Kilvin draws off the heat of a disastrous fire with sympathy then quickly (albeit painfully) stores it in a "heat eater", AKA heat-sink. Kvothe later uses a crude heat sink to draw off the heat of a fire while fighting a dragon and helping to save a town.
Lodenstones, or lode-stones (another name for magnets) are mentioned early on in a discussion of waystones. One later becomes key to Kvothe's defeat of a dragon.
Chekhov's Skill: After his parents die, Kvothe spends the summer in the forest playing his lute, and keeps playing as the strings break one by one. That skill comes in handy when, during an important performance several years later, Ambrose tries to sabotage him by breaking one of his lute strings mid-song.
Circus Brat: Kvothe grew up in a traveling theater troupe, which is pretty close.
Contemptible Cover: Tell me, if you saw this cover◊ without context, would you think it was a serious fantasy book or a romance novel? Luckily, the hardcover came with two covers, the other of which (pictured above) was much more respectable.
Cool Old Guy: Abenthy (mentioned to be pushing sixty) speaks the titular name of the wind on his very first appearance, and he's the one who first teaches Kvothe about sympathy.
Fatal Flaw: Impatience seems to be Kvothe's fatal flaw. A hell of a lot of the trouble he gets himself into could have been avoided oh so easily if he's only bided his time. Most of the rest of the trouble he lands himself in can be put down to his pride and refusal to back down in his feud with Ambrose.
Fearless Fool: Referenced. Kvothe says that only priests and fools are fearless.
Foreshadowing: Lots of it, as it's the first of a trilogy, but a minor (and tragic) example: the early discussion about knacks (unexplainable passive magical talents, essentially), and how those who had them used to be burned in the old days. It is then revealed that Trip, one of Kvothe's fellow troupe members, has the knack of always rolling sevens. Seems like just a bit of world building, until all seven Chandrian (it is hinted they usually only appear in small groups) attack the troupe, killing everyone. Trip's tent had been dragged into the campfire. Yep, lucky.
My Girl Is a Slut: While it's suggested that Denna usually abandons relationships whenever the men try to coerce her into having sex with them, she does kiss and flirt with one after another practically as a way of making a living, even while simultaneously romancing Kvothe. Kvothe, who has not even done that much with her, consoles himself with the knowledge that none of those men have the emotional connection with her that he does.
Nice Job Breaking It, Hero: The Draccus might never have burned down half of Trebon if Kvothe hadn't fed it the denner resin and caused it to go insane. However, the Draccus was already manically looking for more denner resin anyway.
Our Dragons Are Different: The Common Draccus, a flightless, herbivorous lizard which collects rocks in its gizzard to help it digest. It's essentially an elephant-sized cow that breathes fire. The climax reveals that they're not immune to overdosing on an opium-like drug and going on a rampage. Chasing the dragon indeed.
Perpetual Poverty: A continuing theme is that Kvothe is nearly broke and just barely manages to get his tuition paid and his survival needs met.
Secret Test of Character: Used to hilarious effect by Elodin, who tells Kvothe that, if Kvothe wants to become his student and study the secret of Naming (particularly the Name of the Wind), Kvothe will have to jump off this roof. Kvothe assumes that Elodin will catch him with magic. He doesn't. And then he claims Kvothe failed the test by proving himself too reckless to study the subject.
Elodin: "Congratulations. That was the stupidest thing I've ever seen. Ever."
No one seems able to agree on who or what the Chandrian are, and even the ways to identify them vary from story to story.
Also, Kvothe himself. In the Framing Device, the Chronicler has traveled for days to find him, and Kvothe has a Badass Boast about his own history. During his life story, we find out that a lot of the myths surrounding him were started by accident, while he was a student.
Single-Target Sexuality: Despite impressing every music-loving female in Imre with his singing and playing, as well as personally saving the life of a buxom girl and being an all-around charmer besides, Kvothe is hopelessly infatuated with Denna.
Snipe Hunt: While Kvothe is petitioning to be Elodin's apprentice, Elodin tries to get rid of him by sending him after some pinecones.
Starving Student: Kvothe's struggle to come up with his tuition money drives a large part of the plot.
The Stoic: Lorren. According to Simmon, Elxa Dal has a standing offer of 10 gold marks (100 silver talents) for anyone who can make Lorren laugh. So far, Kvothe has managed to make him barely smile ... once.
Sufficiently Analyzed Magic: Sympathy and Alchemy, both of which do things that are truly impossible despite still doing business with physics and chemistry respectively. They're so well analyzed that calling them magic at the University is like saying the sun is pulled by a chariot.
Tempting Fate: Kvothe's parents continue practicing their song about the Chandrian, even after Abenthy warned them.
Too Clever by Half: Kvothe talks his way into his world's premier university at the age of fifteen, after having spent three years as a beggar, and promptly antagonizes both one of the masters and the wealthiest and most politically connected student in the university. Between that and his perpetual poverty, he spends most of his time doing absurd things (learning an entire language in a day and a half, getting certified as a musician on a lute with a broken string) just to keep his head above water.
Writers Cannot Do Math: When Kvothe takes his University entrance exam, the mathematics master asks for the length of the third side of a triangle with a sixty-degree angle between sides of 3 feet and 7 feet. Kvothe's answer, "Six feet six inches, dead even", is accepted as correct... except that the answer is actually the square root of 37, which is slightly less than six foot one inch. Even given that he's doing it in his head, he really should have known the answer was closer to 6 feet than 6.5 feet. Since the square root of 37 is irrational, there's no possible way for "six feet six inches" to be exactly correct, unless they use some strange sort of inch that's an irrational multiple of a foot.